Question

Helium has a mass number 4 and the atomic number 2. Calculate the nuclear binding energy per nucleon. (mass of neutron=1.00893amu and proton=1.00814amu, He=4.0039amu and mass of electron is negligible).

Answer 1

Hint: Neutrons and protons are attracted through strong nuclear force, binding energy is a positive number because it requires energy to overcome this strong nuclear force. The mass of an atomic nucleus is less than the sum of the individual masses.

Complete answer: or Complete step by step answer:
The binding energy (BE) of a nucleus is equal to the amount required to split a nucleus of an atom into its component parts that are protons and neutrons(nucleons), or the mass defect multiplied by the speed of light squared. The binding energy is always a positive value, since all energy is required to separate them into individual protons and neutrons.
The actual mass is always less than the sum of the individual masses of the constituent because energy is removed when the nucleus is formed. The given energy has mass which is removed from the total mass of the original particles. This mass, is known as mass defect, is missing from the resulting nucleus and represents the energy released when the nucleus is formed.

Mass defect (${{M}_{d}}$) is calculated by the difference between observed mass (${{m}_{atom}}$) and expected mass from the combination of protons.(\[{{m}_{p}}\]) and neutrons (${{m}_{n}}$).
\[{{M}_{d}}=[Z({{m}_{p}}+{{m}_{e}})+(A-Z){{m}_{n}}]-{{m}_{atom}}\]
${{m}_{e}}$= mass of electron
Z=atomic number
A= mass number
${{m}_{atom}}$= is the observed mass of nuclide

B.E. = (931.5Mev) x (${{M}_{d}}$)

Given value of mass of proton is,${{m}_{p}}$= 1.00814amu
Mass of neutron is,${{m}_{n}}$= 1.00893amu
Mass of atom is, ${{m}_{atom}}$=4.0039amu Putting the values in the formula of binding energy,

\[\begin{align}
  & {{M}_{d}}=(4.0039-2\times 1.0081-2\times 1.00893) \\
 & \Rightarrow {{M}_{d}}=-0.03016 \\
\end{align}\]

Putting the value of mass defect in the formula of binding energy , we get,
B.E. = (931.5Mev)X(0.03016)
B.E.= −28.094
B.E./nucleon = $\frac{28.094}{4}$
B.E./nucleon = −1.038Mev
Therefore, Binding energy per nucleon for helium atoms is −1.038Mev.

Note:
The mass of the electron is negligible therefore, it is mostly ignored in calculation of mass defect. Binding energy of an atom is not the same for binding energy for the nucleus. The mass defect of a nucleus represents the amount of mass equivalent to the binding energy of the nucleus.